The variation of the superconducting transition temperature T(,c) with hydrostatic pressure up to 23.7 kbar is reported for eleven compounds with the Sc(,5)Co(,4)Si(,10)-type structure. Most of these compounds display a modest linear depression of T(,c) with pressure (dT(,c)/dp (TURN) 10('-5) K/bar), however, two materials, Lu(,5)Ir(,4)Si(,10) and Lu(,5)Rh(,4)Si(,10), undergo a discontinuous transformation above a critical pressure of about 20 kbar to a state with a significantly higher T(,c);The resistivity and magnetic susceptibility show an anomaly in Lu(,5)Ir(,4)Si(,10) and Lu(,5)Rh(,4)Si(,10) at T(,o) = 83 K and 155 K respectively. It is interpreted that this phase transformation may involve a charge density wave (CDW) formation that opens an energy gap over a portion of the Fermi surface. The P-T phase diagram for Lu(,5)Ir(,4)Si(,10), given to demonstrate the correlation between T(,o) and T(,c), provides the clear evidence that the pressure enhancement of T(,c) is due to a progressive removal of the charge density wave in the crystal;Combining the magnetic susceptibility and heat capacity data, we give a quantitative estimate of a 36% loss in the electronic density of states at the Fermi level due to this energy gap in Lu(,5)Ir(,4)Si(,10);The pseudoternary system (Lu(,1-x)Sc(,x))(,5)Ir(,4)Si(,10), 0 (LESSTHEQ) x (LESSTHEQ) 0.05, is used to study the doping (impurity) effect on the CDW and the competition between T(,o) and T(,c) in Lu(,5)Ir(,4)Si(,10). It is found that (dT(,o)/dx)(,x=0) = -18.5 K/at % and (dT(,c)/dx)(,x=0) = 0.5 K/at %, are comparable to another CDW system (Ta(,1-x)Nb(,x))S(,3);The electrical and magnetic properties for R(,5)Ir(,4)Si(,10) (R = Dy-Yb) are also reported. All of these compounds exhibit an anomaly in resistivity, which is considered to be due to the formation of a CDW, similar to the one observed in Lu(,5)Ir(,4)Si(,10). Two distinct magnetic transitions with different features, seen in the ac magnetic susceptibility and heat capacity at low temperature for Tm(,5)Ir(,4)Si(,10) indicate two different types of magnetic structure. Strong crystal field effects or valence fluctuations are suggested to occur in Yb(,5)Ir(,4)Si(,10);because of the noticeable deviation of the magnetic susceptibility from Curie-Weiss law below 70 K; *DOE Report IS-T-1281. This work was performed under contract No. W-7045-Eng-82 with the U.S. Department of Energy.